Winklevoss Bitcoin Trust would initially sell $20m of shares, with each share worth a fraction of a Bitcoin, a filing with US regulator the Securities and Exchange Commission showed.

Bitcoins are a form of electronic money not managed by a single company or government. They are "mined" by people anywhere in the world setting up their computers to compete to solve a complex computing problem for a reward of Bitcoins. Their release is tightly controlled, mimicking a central banking system's control over the minting of money. The system will allow only 21m Bitcoins to exist – by gradually decreasing the size of the "mining" reward.

The value of a Bitcoin has been extremely volatile since the start of the year, rising from $13 in January to a peak of $266 in April and back down to about $100 last week.

Bitcoins have been touted by some as the future of money and gained in prominence during the eurozone sovereign debt crisis as more people questioned the safety of holding their cash in a bank.

But others dismiss the currency as a Ponzi scheme, and authorities worry about its lack of regulation and possible use in money laundering. In May, US authorities seized two accounts linked to a major operator in the Bitcoin digital currency market.

Cameron and Tyler Winklevoss, whose feud with Zuckerberg was portrayed in the fictionalised 2010 film The Social Network, have amassed nearly $11m worth of Bitcoins, according to a report in the New York Times in April.

The identical twins settled the suit with Facebook in a 2008 deal for cash and stock then valued at $65m.